The goal of the proposed project is to develop several new coarse-grained computational models to describe protein structures and protein dynamics. These innovations will let us approach much larger structures, as well as to comprehend important functional behaviors more readily. The realization of the proposed project might be extremely important for the development of computational cell biology and for practical applications in drug design. The project focuses on three specific aims: Specific Aim I: Study protein dynamics using the Gaussian Network Model and Anisotropic Network Model. We will develop a mixed coarse-grained method where the 'interesting' or functional parts of proteins are modeled at a higher resolution than the remainder of the structure. By using this approach, normal mode analysis can be performed to discern the important functional motions with high computational efficiency for large biologically important molecules. Specific Aim II: Develop an extremely efficient transfer matrix method for attrition-free generation of lattice proteins on the square lattice in 2-dimensions and for the cubic lattice in 3-dimensions. The proposed method is an extension of the transfer matrix method for generating and the enumerating compact self-avoiding walks on lattices previously developed by the project's investigators. Specific Aim Ill: Conduct an off-lattice study of the dependencies between protein shapes and their conformations. The goal is to generate libraries of possible three-dimensional protein structures using a minimal set of assumptions. We constrict the shape of the protein within a three-dimensional ellipsoid of revolution and generate all possible compact protein conformations within the shape. We will also study in a systematic way the interdependence between the structures and the shapes of the proteins, as well as their dynamics with the Gaussian Network Models developed in the Specific Aim 1. These findings open the way for more abstract and mathematical representations of biological structure that can lead directly to a better and more complete comprehension of structure and function.